I do have a couple of restaurants to recommend (came back from NY earlier this week) though nothing exotic, unfortunately, since my children don't like sushi, Indian cuisine, etc. (but I'm working on it). Let me try to dig out the addresses. Except for one they're all midtown (i.e. rather touristy, I guess), but food + service were excellent.
1. Lunella Ristorante, 173 Mulberry St. (between Grand & Broome Sts), Little Italy
I just read some of the reviews on TripAdvisor, and I see they range from "excellent" to "dreadful". All I can say is that we had an excellent meal and that I certainly didn't think we'd been ripped off. The front part of the restaurant is rather dark but the back room has a high glass ceiling so it's nice and bright.
2.
Bond 45. This was the most expensive and probably the most touristy of the lot but the food was excellent. Great fish and seafood, and the tiramisù easily feeds two (it even says on the menu that it's "to share"). We went there early (7pm or so) and it was rather quiet (=very pleasant) but by the time we started demolishing said tiramisù the place was heaving and I found the noise level too high for comfort.
Funnily enough, they had a (s)light problem with their outside sign and I couldn't resist taking a picture (although I prefer jokes that are a bit more subtle). Taken from a moving car so it's quite blurred, but still legible...